Question

A cricket team of 11 players is to be selected from two groups of 6 and 8 players. In how many ways can the selection be made so that at least 4 players are taken from the group of 6.

Answer 1

Answer on Question #78456 – Math – Combinatorics | Number Theory

Question

A cricket team of 11 players is to be selected from two groups of 6 and 8 players. In how many ways can the selection be made so that at least 4 players are taken from the group of 6.

Solution

The possible ways of performing the required selection:

a) 4 players from G6 and 7 players from G8;

b) 5 players from G6 and 6 players from G8;

c) 6 players from G6 and 5 players from G8;

Now one needs to determine the number of possible selections for each case.

a) ${}_{6}{C}_{4} \cdot {}_{8}{C}_{7} = \frac{6!}{4!2!} \cdot \frac{8!}{7!1!} = {120}$

b) ${}_{6}{C}_{5} \cdot {}_{8}{C}_{6} = \frac{6!}{5!1!} \cdot \frac{8!}{6!2!} = {168}$

c) ${}_{6}{C}_{6} \cdot {}_{8}{C}_{5} = \frac{6!}{6!0!} \cdot \frac{8!}{5!3!} = {56}$

The total number of selections = 120 + 168 + 56 = 344

Answer: 344 ways of making the given selection.

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